How are quads converted to tris for games?
All 3d applications renders geometry as a bunch of Tris in the end. The Quads and N-gons are only a convenience for editing and gets converted by the render engine. 

When you export models for a game engine you can export them without triangulate them. Most game engines will have the ability to triangulate by them self. The exported file such as FBX or OBJ does not get triangulated automatically.

The way different software chooses to split polygons differs so you really don't have that much control.

There are benefits of doing the triangulation explicitly in Blender: You know how your polygons are split so the normals will look as you intend them to. If you bake normal maps, High to Low, this matters. If you have an animated mesh you usually want to make sure that the meshes and textures deforms in a known way.

I usually add a Triangulate Modifier to my mesh and split the ones I care about manually. In this way I can get a preview of how the triangulation will look at when exported and I get to work with a (mostly) quad mesh that are way easier to work with.